Stagnation point

Photo showing stagnation point and attached vortex at an un-faired wing-root to fuselage junction on a Schempp-Hirth Janus C glider

In fluid dynamics, a stagnation point is a point in a flow field where the local velocity of the fluid is zero.Template:Rp The Bernoulli equation shows that the static pressure is highest when the velocity is zero and hence static pressure is at its maximum value at stagnation points: in this case static pressure equals stagnation pressure.Template:Rp

The Bernoulli equation applicable to incompressible flow shows that the stagnation pressure is equal to the dynamic pressure and static pressure combined.Template:Rp In compressible flows, stagnation pressure is also equal to total pressure as well, provided that the fluid entering the stagnation point is brought to rest isentropically.Template:Rp

A plentiful, albeit surprising, example of such points seem to appear in all but the most extreme cases of fluid dynamics in the form of the "no-slip condition" - the assumption that any portion of a flow field lying along some boundary consists of nothing but stagnation points (the question as to whether this assumption reflects reality or is simply a mathematical convenience has been a continuous subject of debate since the principle was first established).

Pressure coefficient

This information can be used to show that the pressure coefficient $C_p$ at a stagnation point is unity (positive one):Template:Rp

$C_p=\frac{p-p_{\mathrm{\infty }}}{q_{\mathrm{\infty }}}$

where:

$C_p$ is pressure coefficient

$p$ is static pressure at the point at which pressure coefficient is being evaluated

$p_{\mathrm{\infty }}$ is static pressure at points remote from the body (freestream static pressure)

$q_{\mathrm{\infty }}$ is dynamic pressure at points remote from the body (freestream dynamic pressure)

Stagnation pressure minus freestream static pressure is equal to freestream dynamic pressure; therefore the pressure coefficient $C_p$ at stagnation points is +1.Template:Rp

Kutta condition

On a streamlined body fully immersed in a potential flow, there are two stagnation points—one near the leading edge and one near the trailing edge. On a body with a sharp point such as the trailing edge of a wing, the Kutta condition specifies that a stagnation point is located at that point. The streamline at a stagnation point is perpendicular to the surface of the body.

See also

• Stagnation point flow